A BENDIXSON-TYPE THEOREM WITH APPLICATION

Zhao Qingyu Wei Baorong Ding Changming(Department of Mathematics)

In this Paper, at first we discuss the nonexistence of closed orbits for irreduciblecompetitive or cooperative system X = F(X) . X∈U, F∈C' (U) .where U is an open P -convex set in R3.secondly deal with the existence and stability of closed orbits for non-negative feedback system x1 = f (x3) -a1x1,x2 = x1 - a2x2,x3=x2-a3x3,where 0a1.for i - 1,2,3,f'(x3)≤0 for x3≥0.